Spectroscopic analysis of LiTm${\mathrm{F}}_4$

The absorption spectra of ${\mathrm{Tm}}^{3+}$ in LiTm${\mathrm{F}}_4$ have been measured at 2, 10, 30, and 50 K in the spectral interval 4000-25 000 ${\mathrm{cm}}^{-1\mathrm{}}$. The energy levels of the ground-state configuration were calculated by diagonalizing the Hamiltonian of the electron-electron interaction, the spin-orbit coupling, and the crystal field in a basis of the whole configuration. The electrostatic parameter $F_2$, the spin-orbit parameter $\zeta$, and the crystal-field parameters $B_{\mathrm{kq}}$ were varied to obtain the best agreement with the experimentally observed levels. As the model does not account for configuration mixing and minor magnetic effects, it was necessary after optimizing $F_2$ and $\zeta$ to match the centers of gravity for the multiplets before the final adjustment of the $B$ parameters. When this was done, the standard deviation was lowered from 170 to 12 ${\mathrm{cm}}^{-1\mathrm{}}$. The $B$ parameters obtained for ${\mathrm{Tm}}^{3+}$ have been compared to those of ${\mathrm{Tb}}^{3+}$, ${\mathrm{Ho}}^{3+}$, and ${\mathrm{Er}}^{3+}$ in LiLn${\mathrm{F}}_4$, and they follow a common trend. The intensities of the transitions from the ground state were calculated in the Judd-Ofelt scheme, fitting six complex intensity parameters $A\left(kq\lambda \right)$ for best agreement with the experimentally observed intensities. The model was only able to give a rough estimate of the transition probabilities. The obtained relative standard deviation was 1.1. Contrary to what was found in the case of the energy calculations, it was important for the intensity calculations that the $B$ parameters were allowed to take complex values. The imaginary part of the $A$ parameters was not important to the intensities.